We show that the matrix element of a local quark-gluon operator in the photon state, 〈γ(kλ)|Ô|γ(kλ)〉 can be calculated in lattice QCD when there exists a energy gap between the photon and the hadronic states. The result is generalized to other quantities involving space-like photons such as the transition form factor γγ*→π0 and the virtual-photon-nucleon Compton amplitude 〈γ*N |γ*N〉. Using this result, the first moment of the photon structure function, 〈x〉γ=∫01dx F2γ(x,Q2) on β=6.0 quenched lattices is measured and compared with theoretical predictions and the experimental results.
"Studying hadronic structure of the photon in lattice QCD," Xiangdong Ji and Chulwoo Jung, Phys. Rev. Lett. 86, 208 (2001) , hep-lat/0101014.